Item Analysis of GEPD Teacher Knowledge Module - Peru
Brian Stacy
2019-11-05
Abstract
Using GEPD data from Peru, this paper examines the psychometric properties of the mathematics portion of the teacher assessment module. We estimate a two parameter logistic (2PL) item response theory (IRT) model. We produce item characteristic curves (ICC) and test characteristic curves from this model. We then compare our results to data from a similar assessment used in the Service Delivery Indicators project in several Sub-Sahara African countries using an item equating approach.
Takeaways:
- Teachers scored around 43% of our language items correct on average and 61% of our math items
- Our most difficult section was the “correct the letter” sub-task in Language
- We had very few cases of missing values in our assessment
- Our test reliability is above 0.9 at the center of the math and language latent subject knowledge distributions
- Test reliability drops off significantly in math in the tails of the latent math knowledge distribution
- This is consistent with previous experience using SDI survey
- Teachers in Peru scored in the middle of the pack compared to SDI countries in Language
- Peru scored on average above Morocco, Mozambique, but behind Kenya, Lao PDR, Madagascar, and Tanzania in the language assessment.
- Teachers in Peru scored in the middle of the pack compared to SDI countries in Math
- Peru teachers on average outperformed teachers in Mozambique and Madagascar, but behind teachers in Kenya, Tanzania, Morocco, and Lao PDR in the math assessment.
Methodological Approach
We use a model from Item Response Theory (IRT) to examine the functioning of the teacher knowledge test items for Language and Mathematics. The model used is the Two Parameter Logistic (2PL), which allows for items with binary responses (Correct/Incorrect) The model is as follows for item i and person j:
\[ P(u_{ij}=1|\theta_j,\omega)=\frac{exp(a_i(\theta_j - b_{i} ))}{1+exp(a_i(\theta_j - b_{i} ))} \]
Summary Statistics of Data
Before estimating the model, we begin by examining summary statistics and missing values in our item response data. To begin, we will show summary statistics of the fraction correct on the language and math sections of the examination, as well as the fraction correct on broad sub-domains.
The sub-domains for the language section are:
- Correct the letter: teachers are asked to correct a hypothetical letter written by a student for grammar and punctuation.
- Cloze task: teachers are asked to grade a hypothetical student’s cloze task, where the student fills in an appropriate word in a sentence.
- Grammar task: teachers are asked to grade a hypothetical student’s grammar task, where students are asked to fill in a grammatically correct word into a sentence
- Read the passage: teachers are asked to grade a hypothetical student’s read the passage task, where students are asked questions about a passage
The sub-domains for the math section are:
- Arithemtic and number relations: teachers grade a students work in arithemtic, number relations
- Geometry: teachers grade a students work on geometric problems
- Interpret Data: teachers grade a students work interpretting a diagram and data
## Joining, by = "name"| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| cloze | Cloze task | 0.62 | 0.26 | 0 | 0.45 | 0.73 | 0.82 | 1 | 377 | 0 | ▂▂▅▂▃▇▅▅ |
| grammar | Grammar task | 0.81 | 0.23 | 0 | 0.67 | 0.83 | 1 | 1 | 377 | 0 | ▁▁▁▂▁▃▅▇ |
| literacy_content_knowledge | Fraction correct language | 0.7 | 0.2 | 0 | 0.6 | 0.75 | 0.85 | 1 | 377 | 0 | ▁▁▁▃▅▇▆▆ |
| read_passage | Read the passage | 0.79 | 0.31 | 0 | 0.67 | 1 | 1 | 1 | 377 | 0 | ▁▁▁▁▁▃▁▇ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher language assessment. |
## Joining, by = "name"| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| arithmetic_number_relations | Arithmetic and number relations | 0.64 | 0.25 | 0.071 | 0.43 | 0.64 | 0.86 | 1 | 384 | 0 | ▂▃▂▅▇▃▇▅ |
| geometry | Geometry | 0.66 | 0.31 | 0 | 0.5 | 0.75 | 1 | 1 | 384 | 0 | ▁▅▁▅▁▅▁▇ |
| interpret_data | Interpret Data | 0.67 | 0.29 | 0 | 0.4 | 0.8 | 0.8 | 1 | 384 | 0 | ▂▃▁▅▆▁▇▆ |
| math_content_knowledge | Fraction correct math | 0.65 | 0.24 | 0.043 | 0.48 | 0.7 | 0.87 | 1 | 384 | 0 | ▁▃▅▅▃▇▇▅ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher math assessment. |
Item Level Summary Statistics
Next, we display summary statistics at the item level for our language and mathematics assessment.
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s1q1a_grammer | (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. | 0.57 | 0.5 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▆▁▁▁▁▁▁▇ |
| m5s1q1b_grammer | (When, If, Because, Although) I was telling the truth, my mother didn’t believe | 0.8 | 0.4 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q1c_grammer | A person who (which, who, when, may) flies an airplane is a pilot. | 0.85 | 0.36 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q1d_grammer | My sister likes to read, so (so, although, perhaps, when) I have boug | 0.9 | 0.3 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q1e_grammer | If I were a doctor, I shall (will, would, shall, am able to) work i | 0.79 | 0.41 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q1f_grammer | The accident had seen (see, saw, had seen, was seen) by three people | 0.93 | 0.26 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q2a_cloze | Javid, it is (a) half past seven. | 0.59 | 0.49 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2b_cloze | Get (b) . | 0.29 | 0.45 | 0 | 0 | 0 | 1 | 1 | 377 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s1q2c_cloze | Today there is a (c) big football match at school. | 0.64 | 0.48 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2d_cloze | Juma: Father, I (d) want not go to school. | 0.66 | 0.47 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2e_cloze | I am (e) scared to go. | 0.89 | 0.32 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q2f_cloze | Everyone (f) hates me. | 0.64 | 0.48 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2g_cloze | The players want to beat (g) . | 0.77 | 0.42 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s1q2h_cloze |
|
0.32 | 0.47 | 0 | 0 | 0 | 1 | 1 | 377 | 0 | ▇▁▁▁▁▁▁▅ |
| m5s1q2i_cloze | Father: You are going and that is final. I will give you two (i) | 0.62 | 0.49 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▆▁▁▁▁▁▁▇ |
| m5s1q2j_cloze | have to go to school today. First, you are 40 (j) years old. | 0.71 | 0.45 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2k_cloze | Javid, it is (a) half past seven. | 0.71 | 0.45 | 0 | 0 | 1 | 1 | 1 | 377 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q4a_passage | 4a. Why did the animals huddle together beneath the bushes? | 0.81 | 0.39 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q4b_passage | 4b. “His big eyes widened like saucers.” What do these words from the story tell | 0.84 | 0.37 | 0 | 1 | 1 | 1 | 1 | 377 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q4c_passage | 4c. What made the roaring sound in the distance? | 0.72 | 0.45 | 0 | 0 | 1 | 1 | 1 | 376 | 1 | ▃▁▁▁▁▁▁▇ |
| m5sb_tnum | Please enter Teacher’s roster number | 6.6 | 5.54 | 1 | 2 | 5 | 10 | 20 | 377 | 0 | ▇▃▁▁▁▁▁▁ |
| school_code | NA | 530182.84 | 323884.99 | 62181 | 283416 | 436493 | 662346 | 1731926 | 377 | 0 | ▅▇▃▂▁▁▁▁ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher language assessment. |
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s2q10a_data | 10a. Look at the graph. How far has Joe ridden after 6 hours? | 0.72 | 0.45 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s2q10b_data | 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? | 0.34 | 0.47 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q11a_number | 11a. √(144= )12 | 0.87 | 0.33 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q11b_number | 11b. 12.15-11.83= 0.32 | 0.82 | 0.39 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q11c_number | 11c. 3/4÷7/8= 21/32 | 0.43 | 0.5 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▅ |
| m5s2q12_number |
|
0.45 | 0.5 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q13a_geometric | 13a. (a) Perimeter: | 0.55 | 0.5 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▆▁▁▁▁▁▁▇ |
| m5s2q13b_geometric | 13b. (b) Area: 90 cm2 | 0.49 | 0.5 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▇ |
| m5s2q1a_number | 1a. 5/8 +1/4= 6/12 | 0.44 | 0.5 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q1b_number | 1b. √36- √9= √27 | 0.51 | 0.5 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▇ |
| m5s2q1c_number | 1c. 343+215+127= 685 | 0.9 | 0.3 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q1d_number | 1d. 72÷9= 7 | 0.69 | 0.46 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s2q1e_number | 1e. 37×13 = 3711 | 0.72 | 0.45 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s2q2_number |
|
0.75 | 0.43 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q3_number |
|
0.85 | 0.36 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q4a_number | 4a. Complete these fractions so that they are equivalent | 0.49 | 0.5 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q4b_number | 4b. Complete these fractions so that they are equivalent | 0.4 | 0.49 | 0 | 0 | 0 | 1 | 1 | 384 | 0 | ▇▁▁▁▁▁▁▅ |
| m5s2q5_number |
|
0.7 | 0.46 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s2q6_geometric |
|
0.94 | 0.24 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q7_geometric |
|
0.67 | 0.47 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s2q8_data |
|
0.81 | 0.39 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q9a_data | 9a. How many people had cats? | 0.7 | 0.46 | 0 | 0 | 1 | 1 | 1 | 384 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s2q9b_data | 9b. Which animal was the least popular? | 0.78 | 0.42 | 0 | 1 | 1 | 1 | 1 | 384 | 0 | ▃▁▁▁▁▁▁▇ |
| m5sb_tnum | Please enter Teacher’s roster number | 6.84 | 6.75 | 1 | 3 | 5 | 9 | 83 | 384 | 0 | ▇▁▁▁▁▁▁▁ |
| school_code | NA | 534678.72 | 327628.34 | 62181 | 3e+05 | 436493 | 662346 | 1760396 | 384 | 0 | ▃▇▃▂▁▁▁▁ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher math assessment. |
Inter-Item Correlations
Next we display inter-item correlations for our language and math teacher assessment.
Reliability and Confirmatory Factor Analysis
In Psychometrics, internal consistency is an estimate of test reliability. Cronbach’s Alpha (and other internal consistency coefficients) can take values between 0 and 1, being tests more consistent as the value of this coefficient approaches to 1.
In addition to the internal consistency coefficient for a construct, internal consistency analyses also include item level statistics of internal consistency and item discrimination. You will notice in the output of the alpha() function three additional data frames: Reliability if an item is dropped, Item statistics, and Non missing response frequency for each item. We are interested in the first two data frames.
In the case of the data frame “Reliability if an item is dropped”, we need to check what happens with the overall Cronbach’s alpha reliability when a given item is excluded from the analysis. This analysis allows us to identify inconsistent items when Cronbach’s Alpha increases once a given item is excluded. This information will be shown in the first column of that data frame.
In the case of the data frame “Item Statistics”, we want to identify the item correlation with the construct observed total score when the item is excluded from that total score. Ideally, we want items with a positive correlation between each item and the total score, otherwise that item is probably not measuring the same construct as the others, does not correctly discriminate among examinees, or has a problem in either its content or scoring procedure. From this data frame, we are interested in the fifth column titled “r.drop”.
Internal consistency for literacy items. Cronbach’s alpha = 0.80. Good reliability
For each of our language and math constructs (Language: cloze, grammar, read_passage; Math: arithmetic_number_relations, geometry, interpret_data), we report: Cronbach’s alpha for the whole test, Cronbach’s alpha increase or decrease when a given item is removed, and item-total construct score correlation (which is a CTT estimate of item discrimination).
| Cronbach alpha for the whole test | Cronbach alpha increase or decrease when a given item is removed | Item-total construct score correlation | |
|---|---|---|---|
| m5s1q2a_cloze | 0.7953157 | 0.7711747 | 0.5240091 |
| m5s1q2b_cloze | 0.7953157 | 0.8015499 | 0.2291827 |
| m5s1q2c_cloze | 0.7953157 | 0.7631229 | 0.5951171 |
| m5s1q2d_cloze | 0.7953157 | 0.7561969 | 0.6572719 |
| m5s1q2e_cloze | 0.7953157 | 0.7976091 | 0.2292297 |
| m5s1q2f_cloze | 0.7953157 | 0.7639766 | 0.5883499 |
| m5s1q2g_cloze | 0.7953157 | 0.7984915 | 0.2601757 |
| m5s1q2h_cloze | 0.7953157 | 0.7900821 | 0.3517657 |
| m5s1q2i_cloze | 0.7953157 | 0.8066706 | 0.2051435 |
| m5s1q2j_cloze | 0.7953157 | 0.7512813 | 0.6971255 |
| m5s1q2k_cloze | 0.7953157 | 0.7581546 | 0.6383880 |
| Cronbach alpha for the whole test | Cronbach alpha increase or decrease when a given item is removed | Item-total construct score correlation | |
|---|---|---|---|
| m5s1q1a_grammer | 0.6854414 | 0.6526996 | 0.4102313 |
| m5s1q1b_grammer | 0.6854414 | 0.6234375 | 0.4753926 |
| m5s1q1c_grammer | 0.6854414 | 0.7004999 | 0.2330251 |
| m5s1q1d_grammer | 0.6854414 | 0.6593655 | 0.3695725 |
| m5s1q1e_grammer | 0.6854414 | 0.6174713 | 0.4914113 |
| m5s1q1f_grammer | 0.6854414 | 0.6063424 | 0.5746573 |
| Cronbach alpha for the whole test | Cronbach alpha increase or decrease when a given item is removed | Item-total construct score correlation | |
|---|---|---|---|
| m5s1q4a_passage | 0.6902296 | 0.5629543 | 0.5338648 |
| m5s1q4b_passage | 0.6902296 | 0.5863464 | 0.5174464 |
| m5s1q4c_passage | 0.6902296 | 0.6489338 | 0.4749549 |
| Cronbach alpha for the whole test | Cronbach alpha increase or decrease when a given item is removed | Item-total construct score correlation | |
|---|---|---|---|
| m5s2q1a_number | 0.8297789 | 0.8070323 | 0.6186348 |
| m5s2q1b_number | 0.8297789 | 0.8177661 | 0.4801730 |
| m5s2q1c_number | 0.8297789 | 0.8314229 | 0.2262852 |
| m5s2q1d_number | 0.8297789 | 0.8121627 | 0.5590767 |
| m5s2q1e_number | 0.8297789 | 0.8126878 | 0.5524020 |
| m5s2q2_number | 0.8297789 | 0.8194443 | 0.4543922 |
| m5s2q3_number | 0.8297789 | 0.8250594 | 0.3616452 |
| m5s2q4a_number | 0.8297789 | 0.8311211 | 0.3004381 |
| m5s2q4b_number | 0.8297789 | 0.8131696 | 0.5404635 |
| m5s2q5_number | 0.8297789 | 0.8276083 | 0.3385494 |
| m5s2q11a_number | 0.8297789 | 0.8221927 | 0.4159423 |
| m5s2q11b_number | 0.8297789 | 0.8178824 | 0.4797554 |
| m5s2q11c_number | 0.8297789 | 0.8143780 | 0.5245147 |
| m5s2q12_number | 0.8297789 | 0.8109346 | 0.5685776 |
| Cronbach alpha for the whole test | Cronbach alpha increase or decrease when a given item is removed | Item-total construct score correlation | |
|---|---|---|---|
| m5s2q6_geometric | 0.6311091 | 0.7064357 | 0.0918728 |
| m5s2q7_geometric | 0.6311091 | 0.5880060 | 0.3807792 |
| m5s2q13a_geometric | 0.6311091 | 0.3962097 | 0.6023500 |
| m5s2q13b_geometric | 0.6311091 | 0.4185041 | 0.5777277 |
| Cronbach alpha for the whole test | Cronbach alpha increase or decrease when a given item is removed | Item-total construct score correlation | |
|---|---|---|---|
| m5s2q8_data | 0.6532352 | 0.6478732 | 0.2924829 |
| m5s2q9a_data | 0.6532352 | 0.5880597 | 0.4324043 |
| m5s2q9b_data | 0.6532352 | 0.5623142 | 0.4889833 |
| m5s2q10a_data | 0.6532352 | 0.5731189 | 0.4612784 |
| m5s2q10b_data | 0.6532352 | 0.6236595 | 0.3589469 |
IRT Parameters
The tables below show the IRT parameter estimates from our 2PL model.
#create matrix with just item responses
math <- teacher_assessment_math %>%
select(-c(school_code, m5sb_tnum))
language <- teacher_assessment_language %>%
select(-c(school_code, m5sb_tnum))
#Estimate IRT parameters ignoring missing values
irt_math_2PL <- mirt(math, 1, itemtype='2PL', optimizer='NR', SE=FALSE, technical=list(removeEmptyRows=TRUE))##
Iteration: 1, Log-Lik: -4355.076, Max-Change: 0.77616
Iteration: 2, Log-Lik: -4228.942, Max-Change: 0.37144
Iteration: 3, Log-Lik: -4206.642, Max-Change: 0.21762
Iteration: 4, Log-Lik: -4198.099, Max-Change: 0.14399
Iteration: 5, Log-Lik: -4194.128, Max-Change: 0.10103
Iteration: 6, Log-Lik: -4192.154, Max-Change: 0.07305
Iteration: 7, Log-Lik: -4190.146, Max-Change: 0.02099
Iteration: 8, Log-Lik: -4190.057, Max-Change: 0.01610
Iteration: 9, Log-Lik: -4190.007, Max-Change: 0.01214
Iteration: 10, Log-Lik: -4189.943, Max-Change: 0.00302
Iteration: 11, Log-Lik: -4189.940, Max-Change: 0.00223
Iteration: 12, Log-Lik: -4189.938, Max-Change: 0.00167
Iteration: 13, Log-Lik: -4189.932, Max-Change: 0.00102
Iteration: 14, Log-Lik: -4189.932, Max-Change: 0.00091
Iteration: 15, Log-Lik: -4189.932, Max-Change: 0.00082
Iteration: 16, Log-Lik: -4189.930, Max-Change: 0.00033
Iteration: 17, Log-Lik: -4189.930, Max-Change: 0.00030
Iteration: 18, Log-Lik: -4189.930, Max-Change: 0.00027
Iteration: 19, Log-Lik: -4189.930, Max-Change: 0.00011
Iteration: 20, Log-Lik: -4189.930, Max-Change: 0.00010coef(irt_math_2PL, IRTpars=TRUE, as.data.frame=TRUE) %>%
kable() %>%
kable_styling()| par | |
|---|---|
| m5s2q1a_number.a | 2.4442524 |
| m5s2q1a_number.b | 0.2712299 |
| m5s2q1a_number.g | 0.0000000 |
| m5s2q1a_number.u | 1.0000000 |
| m5s2q1b_number.a | 1.3658375 |
| m5s2q1b_number.b | 0.1460926 |
| m5s2q1b_number.g | 0.0000000 |
| m5s2q1b_number.u | 1.0000000 |
| m5s2q1c_number.a | 0.7752071 |
| m5s2q1c_number.b | -2.9958323 |
| m5s2q1c_number.g | 0.0000000 |
| m5s2q1c_number.u | 1.0000000 |
| m5s2q1d_number.a | 1.9000747 |
| m5s2q1d_number.b | -0.7742794 |
| m5s2q1d_number.g | 0.0000000 |
| m5s2q1d_number.u | 1.0000000 |
| m5s2q1e_number.a | 1.9523169 |
| m5s2q1e_number.b | -0.7972886 |
| m5s2q1e_number.g | 0.0000000 |
| m5s2q1e_number.u | 1.0000000 |
| m5s2q2_number.a | 1.3209676 |
| m5s2q2_number.b | -1.1357770 |
| m5s2q2_number.g | 0.0000000 |
| m5s2q2_number.u | 1.0000000 |
| m5s2q3_number.a | 1.1557034 |
| m5s2q3_number.b | -1.6895256 |
| m5s2q3_number.g | 0.0000000 |
| m5s2q3_number.u | 1.0000000 |
| m5s2q4a_number.a | 0.7175522 |
| m5s2q4a_number.b | 0.3781112 |
| m5s2q4a_number.g | 0.0000000 |
| m5s2q4a_number.u | 1.0000000 |
| m5s2q4b_number.a | 2.1269563 |
| m5s2q4b_number.b | 0.4352167 |
| m5s2q4b_number.g | 0.0000000 |
| m5s2q4b_number.u | 1.0000000 |
| m5s2q5_number.a | 0.9669884 |
| m5s2q5_number.b | -0.9234079 |
| m5s2q5_number.g | 0.0000000 |
| m5s2q5_number.u | 1.0000000 |
| m5s2q6_geometric.a | 0.7703682 |
| m5s2q6_geometric.b | -4.3371005 |
| m5s2q6_geometric.g | 0.0000000 |
| m5s2q6_geometric.u | 1.0000000 |
| m5s2q7_geometric.a | 1.2579029 |
| m5s2q7_geometric.b | -0.5923030 |
| m5s2q7_geometric.g | 0.0000000 |
| m5s2q7_geometric.u | 1.0000000 |
| m5s2q8_data.a | 0.9376925 |
| m5s2q8_data.b | -1.8271261 |
| m5s2q8_data.g | 0.0000000 |
| m5s2q8_data.u | 1.0000000 |
| m5s2q9a_data.a | 1.2982132 |
| m5s2q9a_data.b | -0.6858850 |
| m5s2q9a_data.g | 0.0000000 |
| m5s2q9a_data.u | 1.0000000 |
| m5s2q9b_data.a | 1.5972827 |
| m5s2q9b_data.b | -0.9602406 |
| m5s2q9b_data.g | 0.0000000 |
| m5s2q9b_data.u | 1.0000000 |
| m5s2q10a_data.a | 1.6915963 |
| m5s2q10a_data.b | -0.4793811 |
| m5s2q10a_data.g | 0.0000000 |
| m5s2q10a_data.u | 1.0000000 |
| m5s2q10b_data.a | 1.6026208 |
| m5s2q10b_data.b | 0.7214238 |
| m5s2q10b_data.g | 0.0000000 |
| m5s2q10b_data.u | 1.0000000 |
| m5s2q11a_number.a | 1.9791521 |
| m5s2q11a_number.b | -1.4334109 |
| m5s2q11a_number.g | 0.0000000 |
| m5s2q11a_number.u | 1.0000000 |
| m5s2q11b_number.a | 1.7488348 |
| m5s2q11b_number.b | -1.0768108 |
| m5s2q11b_number.g | 0.0000000 |
| m5s2q11b_number.u | 1.0000000 |
| m5s2q11c_number.a | 1.9915238 |
| m5s2q11c_number.b | 0.4719436 |
| m5s2q11c_number.g | 0.0000000 |
| m5s2q11c_number.u | 1.0000000 |
| m5s2q12_number.a | 2.2128578 |
| m5s2q12_number.b | 0.2444848 |
| m5s2q12_number.g | 0.0000000 |
| m5s2q12_number.u | 1.0000000 |
| m5s2q13a_geometric.a | 2.7449964 |
| m5s2q13a_geometric.b | -0.2255125 |
| m5s2q13a_geometric.g | 0.0000000 |
| m5s2q13a_geometric.u | 1.0000000 |
| m5s2q13b_geometric.a | 2.2583454 |
| m5s2q13b_geometric.b | -0.0112839 |
| m5s2q13b_geometric.g | 0.0000000 |
| m5s2q13b_geometric.u | 1.0000000 |
| GroupPars.MEAN_1 | 0.0000000 |
| GroupPars.COV_11 | 1.0000000 |
irt_lang_2PL <- mirt(language, 1, itemtype='2PL',optimizer='NR', SE=FALSE, technical=list(removeEmptyRows=TRUE))##
Iteration: 1, Log-Lik: -3811.491, Max-Change: 0.70531
Iteration: 2, Log-Lik: -3749.645, Max-Change: 0.63370
Iteration: 3, Log-Lik: -3720.109, Max-Change: 0.62401
Iteration: 4, Log-Lik: -3702.372, Max-Change: 0.57622
Iteration: 5, Log-Lik: -3692.954, Max-Change: 0.48877
Iteration: 6, Log-Lik: -3688.568, Max-Change: 0.39341
Iteration: 7, Log-Lik: -3685.132, Max-Change: 0.14437
Iteration: 8, Log-Lik: -3684.965, Max-Change: 0.11910
Iteration: 9, Log-Lik: -3684.865, Max-Change: 0.09931
Iteration: 10, Log-Lik: -3684.666, Max-Change: 0.02787
Iteration: 11, Log-Lik: -3684.653, Max-Change: 0.02056
Iteration: 12, Log-Lik: -3684.645, Max-Change: 0.01600
Iteration: 13, Log-Lik: -3684.627, Max-Change: 0.00492
Iteration: 14, Log-Lik: -3684.624, Max-Change: 0.00464
Iteration: 15, Log-Lik: -3684.622, Max-Change: 0.00416
Iteration: 16, Log-Lik: -3684.615, Max-Change: 0.00162
Iteration: 17, Log-Lik: -3684.615, Max-Change: 0.00148
Iteration: 18, Log-Lik: -3684.615, Max-Change: 0.00136
Iteration: 19, Log-Lik: -3684.614, Max-Change: 0.00070
Iteration: 20, Log-Lik: -3684.614, Max-Change: 0.00061
Iteration: 21, Log-Lik: -3684.614, Max-Change: 0.00054
Iteration: 22, Log-Lik: -3684.614, Max-Change: 0.00025
Iteration: 23, Log-Lik: -3684.614, Max-Change: 0.00024
Iteration: 24, Log-Lik: -3684.614, Max-Change: 0.00022
Iteration: 25, Log-Lik: -3684.614, Max-Change: 0.00012
Iteration: 26, Log-Lik: -3684.614, Max-Change: 0.00010
Iteration: 27, Log-Lik: -3684.614, Max-Change: 0.00009coef(irt_lang_2PL, IRTpars=TRUE, as.data.frame=TRUE) %>%
kable() %>%
kable_styling()| par | |
|---|---|
| m5s1q1a_grammer.a | 0.8175140 |
| m5s1q1a_grammer.b | -0.4677988 |
| m5s1q1a_grammer.g | 0.0000000 |
| m5s1q1a_grammer.u | 1.0000000 |
| m5s1q1b_grammer.a | 0.7618566 |
| m5s1q1b_grammer.b | -1.8055815 |
| m5s1q1b_grammer.g | 0.0000000 |
| m5s1q1b_grammer.u | 1.0000000 |
| m5s1q1c_grammer.a | 0.5917136 |
| m5s1q1c_grammer.b | -2.7363199 |
| m5s1q1c_grammer.g | 0.0000000 |
| m5s1q1c_grammer.u | 1.0000000 |
| m5s1q1d_grammer.a | 1.0994252 |
| m5s1q1d_grammer.b | -2.0339173 |
| m5s1q1d_grammer.g | 0.0000000 |
| m5s1q1d_grammer.u | 1.0000000 |
| m5s1q1e_grammer.a | 0.7478449 |
| m5s1q1e_grammer.b | -1.7889671 |
| m5s1q1e_grammer.g | 0.0000000 |
| m5s1q1e_grammer.u | 1.0000000 |
| m5s1q1f_grammer.a | 1.1217430 |
| m5s1q1f_grammer.b | -2.2350878 |
| m5s1q1f_grammer.g | 0.0000000 |
| m5s1q1f_grammer.u | 1.0000000 |
| m5s1q2a_cloze.a | 1.9152780 |
| m5s1q2a_cloze.b | -0.3935916 |
| m5s1q2a_cloze.g | 0.0000000 |
| m5s1q2a_cloze.u | 1.0000000 |
| m5s1q2b_cloze.a | 0.6198855 |
| m5s1q2b_cloze.b | 1.6619209 |
| m5s1q2b_cloze.g | 0.0000000 |
| m5s1q2b_cloze.u | 1.0000000 |
| m5s1q2c_cloze.a | 2.3269704 |
| m5s1q2c_cloze.b | -0.4367561 |
| m5s1q2c_cloze.g | 0.0000000 |
| m5s1q2c_cloze.u | 1.0000000 |
| m5s1q2d_cloze.a | 3.3052049 |
| m5s1q2d_cloze.b | -0.4486762 |
| m5s1q2d_cloze.g | 0.0000000 |
| m5s1q2d_cloze.u | 1.0000000 |
| m5s1q2e_cloze.a | 0.6677942 |
| m5s1q2e_cloze.b | -3.3581175 |
| m5s1q2e_cloze.g | 0.0000000 |
| m5s1q2e_cloze.u | 1.0000000 |
| m5s1q2f_cloze.a | 2.7182230 |
| m5s1q2f_cloze.b | -0.4360568 |
| m5s1q2f_cloze.g | 0.0000000 |
| m5s1q2f_cloze.u | 1.0000000 |
| m5s1q2g_cloze.a | 0.6450082 |
| m5s1q2g_cloze.b | -1.6262678 |
| m5s1q2g_cloze.g | 0.0000000 |
| m5s1q2g_cloze.u | 1.0000000 |
| m5s1q2h_cloze.a | 1.0258080 |
| m5s1q2h_cloze.b | 0.7698623 |
| m5s1q2h_cloze.g | 0.0000000 |
| m5s1q2h_cloze.u | 1.0000000 |
| m5s1q2i_cloze.a | 0.6118441 |
| m5s1q2i_cloze.b | -0.3279676 |
| m5s1q2i_cloze.g | 0.0000000 |
| m5s1q2i_cloze.u | 1.0000000 |
| m5s1q2j_cloze.a | 5.8873397 |
| m5s1q2j_cloze.b | -0.3622293 |
| m5s1q2j_cloze.g | 0.0000000 |
| m5s1q2j_cloze.u | 1.0000000 |
| m5s1q2k_cloze.a | 4.0690330 |
| m5s1q2k_cloze.b | -0.3807108 |
| m5s1q2k_cloze.g | 0.0000000 |
| m5s1q2k_cloze.u | 1.0000000 |
| m5s1q4a_passage.a | 0.7613037 |
| m5s1q4a_passage.b | -2.1332402 |
| m5s1q4a_passage.g | 0.0000000 |
| m5s1q4a_passage.u | 1.0000000 |
| m5s1q4b_passage.a | 1.0349799 |
| m5s1q4b_passage.b | -1.8045033 |
| m5s1q4b_passage.g | 0.0000000 |
| m5s1q4b_passage.u | 1.0000000 |
| m5s1q4c_passage.a | 0.6568010 |
| m5s1q4c_passage.b | -1.5335950 |
| m5s1q4c_passage.g | 0.0000000 |
| m5s1q4c_passage.u | 1.0000000 |
| GroupPars.MEAN_1 | 0.0000000 |
| GroupPars.COV_11 | 1.0000000 |
#estimate factor scores from models
lang_teach_scores<-data.frame(fscores(irt_lang_2PL, method='EAP', response.pattern = language))
math_teach_scores<-data.frame(fscores(irt_math_2PL, method='EAP', response.pattern = math))
#merge scores back ontoPlots of Test Information Function and Test Reliability Function
Below we plot the test information and test reliability functions estimated from our 2PL IRT model.
Item Information Functions
Below is a plot of the item information functions for all of our math and language items. Specific items can be displayed by using the filters in the sidebars.
SDI Comparison
Next, we examine how teachers in Peru compare to teachers in other countries that have taken a similar examination. The Service Delivery Indicator survey has been deployed in several countries, mostly in Sub-Saharan Africa. The teacher assessment used is very similar to the one used in the Peru Dashboard survey. In fact, the Peru test instrument was taken directly from the SDI instrument, with a few modifications. A ‘read the passage’ item was added to our instrument, which differs from most SDI assessments. Additionally, two arithmetic and number relations math problems on square roots and adding fractions were added to make our math assessment more difficult.
The list of overlapping items is below.
## [1] "The following items in Language overlapped in SDI and the Dashboard:"## [1] "m5s1q1a_grammer" "m5s1q1b_grammer" "m5s1q1c_grammer"
## [4] "m5s1q1d_grammer" "m5s1q1e_grammer" "m5s1q1f_grammer"
## [7] "m5s1q2a_cloze" "m5s1q2b_cloze" "m5s1q2c_cloze"
## [10] "m5s1q2d_cloze" "m5s1q2e_cloze" "m5s1q2f_cloze"
## [13] "m5s1q2g_cloze" "m5s1q2h_cloze" "m5s1q2i_cloze"
## [16] "m5s1q2j_cloze" "m5s1q2k_cloze"## [1] "The following items in Math overlapped in SDI and the Dashboard:"## [1] "m5s2q1c_number" "m5s2q1d_number" "m5s2q1e_number"
## [4] "m5s2q2_number" "m5s2q3_number" "m5s2q4a_number"
## [7] "m5s2q4b_number" "m5s2q5_number" "m5s2q6_geometric"
## [10] "m5s2q7_geometric" "m5s2q8_data" "m5s2q9a_data"
## [13] "m5s2q9b_data" "m5s2q10a_data" "m5s2q10b_data"
## [16] "m5s2q11a_number" "m5s2q11b_number" "m5s2q11c_number"
## [19] "m5s2q12_number" "m5s2q13a_geometric" "m5s2q13b_geometric"In what follows below, we will compare teacher latent ability scores for Peru using our Dashboard Survey to ability scores from the SDI survey in Kenya, Lao PDR, Madagascar, Morocco, Mozambique, and Tanzania.
Methodology for item equating
In order to equate the ability scores produced using the different instruments, we use an IRT equating method based on the common set of items. We use the ‘equateIRT’ R package to do so. https://cran.r-project.org/web/packages/equateIRT/equateIRT.pdf.
The goal of test equating in our case is to place scores from Dashboard survey and the SDI survey on a common scale, so that we can directly compare teacher latent ability across countries. We use the common set of items, listed above, to do the equating. A direct equating approach is used based on the Stocking-Lord approach.
Summary Statistics of Ability Scores
Below we show the distributions of teacher ability scores based on the IRT model estimates.
## Picking joint bandwidth of 0.0452
| countryname | math_content_knowledge_mean | math_content_knowledge_sd |
|---|---|---|
| Kenya | 0.7559985 | 0.2114395 |
| Lao PDR | 0.4543115 | 0.2134898 |
| Madagascar | 0.2312355 | 0.1375563 |
| Morocco | 0.7311888 | 0.2361793 |
| Mozambique | 0.1227382 | 0.2098122 |
| Peru | 0.6696810 | 0.2376182 |
| Tanzania | 0.2675159 | 0.3272945 |
## Picking joint bandwidth of 0.0423
| countryname | literacy_content_knowledge_mean | literacy_content_knowledge_sd |
|---|---|---|
| Kenya | 0.7613109 | 0.1632670 |
| Lao PDR | 0.7203196 | 0.2271848 |
| Madagascar | 0.3798607 | 0.2551291 |
| Morocco | 0.8379144 | 0.1900895 |
| Mozambique | 0.4641791 | 0.1922594 |
| Peru | 0.6867700 | 0.2140706 |
| Tanzania | 0.6851075 | 0.1906235 |
Summary Statistics SDI - Kenya
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s1q1a_grammer | (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. | 0.69 | 0.46 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s1q1b_grammer | (When, If, Because, Although) I was telling the truth, my mother didn’t believe | 0.92 | 0.27 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q1c_grammer | A person who (which, who, when, may) flies an airplane is a pilot. | 0.98 | 0.14 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q1d_grammer | My sister likes to read, so (so, although, perhaps, when) I have boug | 0.92 | 0.27 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q1e_grammer | If I were a doctor, I shall (will, would, shall, am able to) work i | 0.93 | 0.26 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q1f_grammer | The accident had seen (see, saw, had seen, was seen) by three people | 0.94 | 0.23 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q2a_cloze | Javid, it is (a) half past seven. | 0.84 | 0.37 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q2b_cloze | Get (b) . | 0.86 | 0.34 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s1q2c_cloze | Today there is a (c) big football match at school. | 0.62 | 0.48 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2d_cloze | Juma: Father, I (d) want not go to school. | 0.4 | 0.49 | 0 | 0 | 0 | 1 | 1 | 1679 | 0 | ▇▁▁▁▁▁▁▅ |
| m5s1q2e_cloze | I am (e) scared to go. | 0.23 | 0.42 | 0 | 0 | 0 | 0 | 1 | 1679 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s1q2f_cloze | Everyone (f) hates me. | 0.82 | 0.39 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q2g_cloze | The players want to beat (g) . | 0.76 | 0.43 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s1q2h_cloze |
|
0.69 | 0.46 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s1q2i_cloze | Father: You are going and that is final. I will give you two (i) | 0.88 | 0.33 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q2j_cloze | have to go to school today. First, you are 40 (j) years old. | 0.79 | 0.4 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q2k_cloze | Javid, it is (a) half past seven. | 0.68 | 0.47 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▃▁▁▁▁▁▁▇ |
| m6sa1q1a | NA | 0.98 | 0.12 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m6sa1q1b | NA | 0.97 | 0.18 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m6sa1q1c | NA | 0.97 | 0.18 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m6sa1q1d | NA | 0.93 | 0.25 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher language assessment. |
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s2q10a_data | 10a. Look at the graph. How far has Joe ridden after 6 hours? | 0.8 | 0.4 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q10b_data | 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? | 0.45 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1679 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q11a_number | 11a. √(144= )12 | 0.87 | 0.34 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q11b_number | 11b. 12.15-11.83= 0.32 | 0.81 | 0.39 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q11c_number | 11c. 3/4÷7/8= 21/32 | 0.67 | 0.47 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s2q12_number |
|
0.71 | 0.45 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s2q13a_geometric | 13a. (a) Perimeter: | 0.79 | 0.41 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q13b_geometric | 13b. (b) Area: 90 cm2 | 0.73 | 0.44 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▃▁▁▁▁▁▁▇ |
| m5s2q1c_number | 1c. 343+215+127= 685 | 0.88 | 0.33 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q1d_number | 1d. 72÷9= 7 | 0.87 | 0.34 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q1e_number | 1e. 37×13 = 3711 | 0.87 | 0.33 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q2_number |
|
0.77 | 0.42 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q3_number |
|
0.9 | 0.3 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q4a_number | 4a. Complete these fractions so that they are equivalent | 0.4 | 0.49 | 0 | 0 | 0 | 1 | 1 | 1679 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q4b_number | 4b. Complete these fractions so that they are equivalent | 0.47 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1679 | 0 | ▇▁▁▁▁▁▁▇ |
| m5s2q5_number |
|
0.83 | 0.38 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q6_geometric |
|
0.94 | 0.24 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q7_geometric |
|
0.93 | 0.25 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q8_data |
|
0.78 | 0.41 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q9a_data | 9a. How many people had cats? | 0.63 | 0.48 | 0 | 0 | 1 | 1 | 1 | 1679 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s2q9b_data | 9b. Which animal was the least popular? | 0.77 | 0.42 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▂▁▁▁▁▁▁▇ |
| m6sa2q1a | NA | 0.97 | 0.17 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| m6sa2q1b | NA | 0.88 | 0.33 | 0 | 1 | 1 | 1 | 1 | 1679 | 0 | ▁▁▁▁▁▁▁▇ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher math assessment. |
Summary Statistics SDI - Mozambique
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s1q1a_grammer | (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. | 0.13 | 0.34 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s1q1b_grammer | (When, If, Because, Although) I was telling the truth, my mother didn’t believe | 0.33 | 0.47 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s1q1c_grammer | A person who (which, who, when, may) flies an airplane is a pilot. | 0.43 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s1q1d_grammer | My sister likes to read, so (so, although, perhaps, when) I have boug | 0.45 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s1q1e_grammer | If I were a doctor, I shall (will, would, shall, am able to) work i | 0.45 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s1q1f_grammer | The accident had seen (see, saw, had seen, was seen) by three people | 0.45 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s1q2a_cloze | Javid, it is (a) half past seven. | 0.24 | 0.43 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s1q2b_cloze | Get (b) . | 0.14 | 0.35 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s1q2c_cloze | Today there is a (c) big football match at school. | 0.28 | 0.45 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s1q2d_cloze | Juma: Father, I (d) want not go to school. | 0.25 | 0.43 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s1q2e_cloze | I am (e) scared to go. | 0.12 | 0.32 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s1q2f_cloze | Everyone (f) hates me. | 0.15 | 0.36 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s1q2g_cloze | The players want to beat (g) . | 0.15 | 0.36 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s1q2h_cloze |
|
0.041 | 0.2 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s1q2i_cloze | Father: You are going and that is final. I will give you two (i) | 0.02 | 0.14 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s1q2j_cloze | have to go to school today. First, you are 40 (j) years old. | 0.15 | 0.35 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s1q2k_cloze | Javid, it is (a) half past seven. | 0.17 | 0.38 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m6sa1q1a | NA | 0.47 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▇ |
| m6sa1q1b | NA | 0.46 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▇ |
| m6sa1q1c | NA | 0.44 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▆ |
| m6sa1q1d | NA | 0.45 | 0.5 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▆ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher language assessment. |
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s2q10a_data | 10a. Look at the graph. How far has Joe ridden after 6 hours? | 0.11 | 0.32 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q10b_data | 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? | 0.021 | 0.14 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q11a_number | 11a. √(144= )12 | 0.12 | 0.32 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q11b_number | 11b. 12.15-11.83= 0.32 | 0.12 | 0.33 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q11c_number | 11c. 3/4÷7/8= 21/32 | 0.05 | 0.22 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q12_number |
|
0.038 | 0.19 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q13a_geometric | 13a. (a) Perimeter: | 0.062 | 0.24 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q13b_geometric | 13b. (b) Area: 90 cm2 | 0.049 | 0.22 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q1c_number | 1c. 343+215+127= 685 | 0.33 | 0.47 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q1d_number | 1d. 72÷9= 7 | 0.27 | 0.44 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q1e_number | 1e. 37×13 = 3711 | 0.27 | 0.44 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q2_number |
|
0.19 | 0.39 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s2q3_number |
|
0.22 | 0.41 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s2q4a_number | 4a. Complete these fractions so that they are equivalent | 0.051 | 0.22 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q4b_number | 4b. Complete these fractions so that they are equivalent | 0.044 | 0.21 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q5_number |
|
0.13 | 0.33 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q6_geometric |
|
0.25 | 0.43 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q7_geometric |
|
0.23 | 0.42 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s2q8_data |
|
0.11 | 0.31 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q9a_data | 9a. How many people had cats? | 0.1 | 0.31 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q9b_data | 9b. Which animal was the least popular? | 0.14 | 0.35 | 0 | 0 | 0 | 0 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▁ |
| m6sa2q1a | NA | 0.38 | 0.49 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▅ |
| m6sa2q1b | NA | 0.33 | 0.47 | 0 | 0 | 0 | 1 | 1 | 1343 | 0 | ▇▁▁▁▁▁▁▃ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher math assessment. |
Summary Statistics SDI - LAO_PDR
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s1q1a_grammer | (Unless, If, Perhaps, Although) you tidy up your room, you won’t get candy. | 0.44 | 0.5 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s1q1b_grammer | (When, If, Because, Although) I was telling the truth, my mother didn’t believe | 0.41 | 0.49 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s1q1c_grammer | A person who (which, who, when, may) flies an airplane is a pilot. | 0.84 | 0.37 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q1d_grammer | My sister likes to read, so (so, although, perhaps, when) I have boug | 0.8 | 0.4 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q1e_grammer | If I were a doctor, I shall (will, would, shall, am able to) work i | 0.85 | 0.36 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q1f_grammer | The accident had seen (see, saw, had seen, was seen) by three people | 0.78 | 0.41 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s1q2a_cloze | Javid, it is (a) half past seven. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2b_cloze | Get (b) . | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2c_cloze | Today there is a (c) big football match at school. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2d_cloze | Juma: Father, I (d) want not go to school. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2e_cloze | I am (e) scared to go. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2f_cloze | Everyone (f) hates me. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2g_cloze | The players want to beat (g) . | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2h_cloze |
|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2i_cloze | Father: You are going and that is final. I will give you two (i) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2j_cloze | have to go to school today. First, you are 40 (j) years old. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m5s1q2k_cloze | Javid, it is (a) half past seven. | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 740 | 0 | ▁▁▁▇▁▁▁▁ |
| m6sa1q1a | NA | 0.92 | 0.26 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▁▁▁▁▁▁▁▇ |
| m6sa1q1b | NA | 0.83 | 0.37 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m6sa1q1c | NA | 0.79 | 0.41 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m6sa1q1d | NA | 0.93 | 0.26 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▁▁▁▁▁▁▁▇ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher language assessment. |
| Item | Label | Mean | Std Dev | Min | 25th Percentile | Median | 75th Percentile | Max | # Complete Cases | # Missing Cases | Histogram |
|---|---|---|---|---|---|---|---|---|---|---|---|
| m5s2q10a_data | 10a. Look at the graph. How far has Joe ridden after 6 hours? | 0.33 | 0.47 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q10b_data | 10b. Chan started riding at 8.30 in the morning. How far had he gone at 12.00pm? | 0.14 | 0.34 | 0 | 0 | 0 | 0 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q11a_number | 11a. √(144= )12 | 0.22 | 0.41 | 0 | 0 | 0 | 0 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s2q11b_number | 11b. 12.15-11.83= 0.32 | 0.29 | 0.46 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▃ |
| m5s2q11c_number | 11c. 3/4÷7/8= 21/32 | 0.12 | 0.32 | 0 | 0 | 0 | 0 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q12_number |
|
0.1 | 0.31 | 0 | 0 | 0 | 0 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q13a_geometric | 13a. (a) Perimeter: | 0.073 | 0.26 | 0 | 0 | 0 | 0 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▁ |
| m5s2q13b_geometric | 13b. (b) Area: 90 cm2 | 0.17 | 0.38 | 0 | 0 | 0 | 0 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▂ |
| m5s2q1c_number | 1c. 343+215+127= 685 | 0.89 | 0.32 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q1d_number | 1d. 72÷9= 7 | 0.86 | 0.34 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▁▁▁▁▁▁▁▇ |
| m5s2q1e_number | 1e. 37×13 = 3711 | 0.84 | 0.37 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q2_number |
|
0.64 | 0.48 | 0 | 0 | 1 | 1 | 1 | 740 | 0 | ▅▁▁▁▁▁▁▇ |
| m5s2q3_number |
|
0.77 | 0.42 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q4a_number | 4a. Complete these fractions so that they are equivalent | 0.41 | 0.49 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q4b_number | 4b. Complete these fractions so that they are equivalent | 0.37 | 0.48 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▅ |
| m5s2q5_number |
|
0.54 | 0.5 | 0 | 0 | 1 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▇ |
| m5s2q6_geometric |
|
0.8 | 0.4 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| m5s2q7_geometric |
|
0.59 | 0.49 | 0 | 0 | 1 | 1 | 1 | 740 | 0 | ▆▁▁▁▁▁▁▇ |
| m5s2q8_data |
|
0.43 | 0.5 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▆ |
| m5s2q9a_data | 9a. How many people had cats? | 0.51 | 0.5 | 0 | 0 | 1 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▇ |
| m5s2q9b_data | 9b. Which animal was the least popular? | 0.44 | 0.5 | 0 | 0 | 0 | 1 | 1 | 740 | 0 | ▇▁▁▁▁▁▁▆ |
| m6sa2q1a | NA | 0.97 | 0.18 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▁▁▁▁▁▁▁▇ |
| m6sa2q1b | NA | 0.84 | 0.37 | 0 | 1 | 1 | 1 | 1 | 740 | 0 | ▂▁▁▁▁▁▁▇ |
| Note: | |||||||||||
| Summary table shows unweighted summary statistics from teacher math assessment. |